Multiply the following complex numbers, marked as blue dots on the graph: $[5(\cos(\frac{7}{4}\pi) + i \sin(\frac{7}{4}\pi))] \cdot [1]$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $5(\cos(\frac{7}{4}\pi) + i \sin(\frac{7}{4}\pi))$ ) has angle $\frac{7}{4}\pi$ and radius $5$ The second number ( $1$ ) has angle $0$ and radius $1$ The radius of the result will be $5 \cdot 1$ , which is $5$ The angle of the result is $\frac{7}{4}\pi + 0 = \frac{7}{4}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{7}{4}\pi$.